Bibounded uo-convergence and b-property in vector lattices

Alpay, Safak
Emelyanov, Eduard
Gorokhova, Svetlana
We define bidual bounded uo-convergence in vector lattices and investigate relations between this convergence and b-property. We prove that for a regular Riesz dual system ⟨ X, X∼⟩ , X has b-property if and only if the order convergence in X agrees with the order convergence in X∼ ∼.


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Marabeh, Mohammad A. A.; Emel’yanov, Eduard; Department of Mathematics (2017)
The main aim of this thesis is to generalize unbounded order convergence, unbounded norm convergence and unbounded absolute weak convergence to lattice-normed vector lattices (LNVLs). Therefore, we introduce the follwing notion: a net $(x_alpha)$ in an LNVL $(X,p,E)$ is said to be unbounded $p$-convergent to $x in X$ (shortly, $x_alpha$ $up$- converges to $x$) if $p(lvert x_alpha −x rvert wedge u) xrightarrow{o}0$ in $E$ for all $u ∈ X_+$. Throughout this thesis, we study general properties of $up$-converge...
Geometric measures of entanglement
UYANIK, KIVANÇ; Turgut, Sadi (American Physical Society (APS), 2010-03-01)
The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three-qubit case is discussed and it is argued that the distance to the W states is a new monotone.
Coherent states for PT-/non-PT-symmetric and non-Hermitian Morse potentials via the path integral method
KANDIRMAZ, NALAN; Sever, Ramazan (IOP Publishing, 2010-03-01)
We discuss the coherent states for PT-/non-PT-symmetric and non-Hermitian generalized Morse potentials obtained by using path integral formalism over the holomorphic coordinates. We transform the action of generalized Morse potentials into two harmonic oscillators with a new parametric time to establish the parametric time coherent states. We calculate the energy eigenvalues and the corresponding wave functions in parabolic coordinates.
Exact Pseudospin Symmetric Solution of the Dirac Equation for Pseudoharmonic Potential in the Presence of Tensor Potential
AYDOĞDU, OKTAY; Sever, Ramazan (Springer Science and Business Media LLC, 2010-04-01)
Under the pseudospin symmetry, we obtain exact solution of the Dirac equation for the pseudoharmonic potential in the presence of the tensor potential with arbitrary spin-orbit coupling quantum number kappa. The energy eigenvalue equation of the Dirac particles is found and the corresponding radial wave functions are presented in terms of confluent hypergeometric functions. We investigate the tensor potential dependence of the energy of the each state in the pseudospin doublet. It is shown that degeneracy b...
Unbounded order convergence and the Gordon theorem#
Gorokhova, S.G.; Kutateladze, S.S. (2019-01-01)
The celebrated Gordon's theorem is a natural tool for dealing with universal completions of Archimedean vector lattices. Gordon's theorem allows us to clarify some recent results on unbounded order convergence. Applying the Gordon theorem, we demonstrate several facts on order convergence of sequences in Archimedean vector lattices. We present an elementary Boolean-Valued proof of the Gao-Grobler-Troitsky-Xanthos theorem saying that a sequence xn in an Archimedean vector lattice X is uo-null (uo-Cauchy) in ...
Citation Formats
S. Alpay, E. Emelyanov, and S. Gorokhova, “Bibounded uo-convergence and b-property in vector lattices,” Positivity, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: